Results (PhD Chapter 2)

This series of files compile all analyses done during Chapter 2:

All analyses have been done with R 3.6.0.

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Human activities considered for the analyses:

Data is also available for the number of captured individuals for dogwhelk (Buccinum sp.), common crab (Cancer irroratus), snowcrab (Chinoecetes opilio), nordic shrimp (Pandalus borealis), arctic surfclam (Mactromeris polynyma) and american lobster (Homarus americanus) fisheries.

1. Maps

1.1. General map

1.2. Parameters maps

Depth

Isobaths

Slope

2. Modelling of human activities influence

The influence of each human activity has been modelled at each station, in order to be later used in prediction models (see section 2).

We calculated an index of influence for each activity \(I_{ij}\), with an index of exposure \(E_{ij}\) and a specific weighting parameter \(w_{j}\).

\[ I_{ij} = w_{j} . E_{ij} \]

Two categories of exposure indices \(E_{ij}\) were defined and calculated differentely: one for fisheries and one for non-fishery human activities.

2.1. Non-fishery human activities

Here, \(E_{ij}\) have been calculated with the distance from the source(s) of the activity, the bathymetry and the hydrodynamical constraints.

\[ E_{ij} = f_{S} \left( D_{ij}, Z_{i}, H_{i} \right) . S_{j} + f_{M} \left( D_{ij}, Z_{i}, H_{i} \right) . M_{j} + f_{L} \left( D_{ij}, Z_{i}, H_{i} \right) . L_{j} \]

  • \(i\) is a station
  • \(j\) is a human activity
  • \(f_{S}\), \(f_{M}\), \(f_{L}\) are the resistance functions for small, medium and large particles, respectively
  • \(D_{ij}\) is the distance of station \(i\) from the source of activity \(j\)
  • \(Z_{i}\) is the bathymetry at station \(i\)
  • \(H_{i}\) is the hydrodynamic constraint at station \(i\)
  • \(S_{j}\), \(M_{j}\), \(L_{j}\) are the proportions of small, medium and large particles, respectively, for activity \(j\)

2.1.1. Index of exposure

This corresponds to \(E_{ij}\) in Formula 2.

This step is done with the package gdistance. The aim of this step is to model the exposure of the station for each human activity. The exposure will be modelled as particles that can difuse in a certain area. We will establish a connectivity matrix between each cell of the raster, in order to calculate the least-cost path of the particles from the source of an activity to each station.

The connectivity matrix will be based on the “resistance seascape” concept. We will use the bathymetry and the hydrographic constraints to give a cost for the inclusion of a cell to the final path returned. This method will allow to take coasts and islands into consideration, which is necessary at BSI. Two underlying principles are established for this analysis:

  • stations spatially close at a similar depth are more susceptible to respond identically to a human activity than stations at different depths (proximity effect)
  • particles will disperse easily from shallow to deeper depths, while the reverse will be difficult (gravity effect)

This method will be applied to three types of particles, because each activity will not have the same type of diffusion in their environment. Small (S), medium (M) and large (L) theoretical particules will be considered here, and each will have its own resistance function \(f_{S}\), \(f_{M}\) and \(f_{L}\) (based on \(D_{ij}\), \(Z_{i}\) and \(H_{i}\)).

Particle Transition function
Small TBA
Medium TBA
Large TBA

To calculate each \(E_{ij}\), we will sum these three components multiplied by the parameters \(S_{j}\), \(M_{j}\) and \(L_{j}\). These are the proportions of small, medium and large particules involved in the modeling of activity \(j\)’s effect, and they will be defined by us (some literature rewiew will be needed for groundtruthing.)

The following maps present the values of \(E_{ij}\) calculated for each non-fishery activity.

CityInf

InduInf

DredColl

DredDump

MoorSite

RainSew

WastSew

CityWha

InduWha

2.1.2. Weighting parameter

This corresponds to \(w_{j}\) in Formula 1.

The following table shows the weights \(w_{j}\) for each non-fishery human activity:

CityInf InduInf DredColl DredDump MoorSite RainSew WastSew CityWha InduWha
1 1 1 1 1 1 1 1 1

2.1.3. Index of influence

This corresponds to \(I_{ij}\) in Formula 1.

Finally, we can calculate \(I_{ij}\) thanks to the previous calculations.

TO BE FINALIZED.

CityInf

InduInf

DredDump

DredDump

MoorSite

RainSew

WastSew

CityWha

InduWha

2.2. Fisheries

Here, \(E_{ij}\) have been calculated thanks to the database of David Beauchesne.

TO BE ADDED.

2.2.1. Index of exposure

This corresponds to \(E_{ij}\) in Formula 3.

TO BE ADDED.

2.2.2. Weighting parameter

This corresponds to \(w_{j}\) in Formula 1.

The following table shows the weights \(w_{j}\) for each fishery:

FishTrap FishTraw FishLine FishNet FishDred
1 1 1 1 1

2.2.3. Index of influence

This corresponds to \(I_{ij}\) in Formula 1.

Finally, we can calculate \(I_{ij}\) thanks to the previous calculations.

TO BE ADDED.

Elliot Dreujou

2019-10-18